MinT - Information on Result #1523097

Information on Result #1523097

Linear OOA(3¹²⁸, 692, F₃, 3, 31) (dual of [(692, 3), 1948, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹²⁸, 692, F₃, 31) (dual of [692, 564, 32]-code), using

discarding factors / shortening the dual code based on linear OA(3¹²⁸, 760, F₃, 31) (dual of [760, 632, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
  1. linear OA(3¹¹⁸, 729, F₃, 31) (dual of [729, 611, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(3⁹⁷, 729, F₃, 25) (dual of [729, 632, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  3. linear OA(3¹⁰, 31, F₃, 5) (dual of [31, 21, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
      - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.